Polar coordinate drawing of planar graphs with good angular resolution

Christian A. Duncan, Stephen G Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms which use polar representation. The main advantage of using a polar representation is that it allows us to exert independent control over grid size and bend positions. Polar coordinates allow us to specify different vertex resolution, bend-point resolution and edge separation. We first describe a standard (Cartesian) representation algorithm (CRA) which we then modify to obtain a polar representation algorithm (PRA). In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, √2/2 edge separation, 5n × 5n/2 drawing area and 1/2d(v) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of φ/4d(v) 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and √2/2 edge separation), the PRA algorithm creates a drawing of size 9n × 9n/2.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages407-421
Number of pages15
Volume2265 LNCS
StatePublished - 2002
Event9th International Symposium on Graph Drawing, GD 2001 - Vienna, Austria
Duration: Sep 23 2001Sep 26 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2265 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other9th International Symposium on Graph Drawing, GD 2001
CountryAustria
CityVienna
Period9/23/019/26/01

Fingerprint

Polar coordinates
Planar graph
Cartesian
Vertex of a graph
Drawing
Unit

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., & Kobourov, S. G. (2002). Polar coordinate drawing of planar graphs with good angular resolution. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2265 LNCS, pp. 407-421). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS).

Polar coordinate drawing of planar graphs with good angular resolution. / Duncan, Christian A.; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS 2002. p. 407-421 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Duncan, CA & Kobourov, SG 2002, Polar coordinate drawing of planar graphs with good angular resolution. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2265 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2265 LNCS, pp. 407-421, 9th International Symposium on Graph Drawing, GD 2001, Vienna, Austria, 9/23/01.
Duncan CA, Kobourov SG. Polar coordinate drawing of planar graphs with good angular resolution. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS. 2002. p. 407-421. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Duncan, Christian A. ; Kobourov, Stephen G. / Polar coordinate drawing of planar graphs with good angular resolution. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS 2002. pp. 407-421 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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